We use the Python implementation of group LASSO [1]} by Yngve Mardal Moe at the University of Oslo that can be found at https://group-LASSO.readthedocs.io/en/latest/index.html.
We select among 2210 sensor measurements of \(u\)  and \(v\)  velocity components over a grid of 1105 spatial locations taken directly from the shock-mixing layer snapshot data.
We tried two different kinds of target variables to be reconstructed via group LASSO.
For the method we call “LASSO+PCA”, the target variables were the data's leading 100 principal components which capture over \(99\%\)  of the data's variance.
For the method we call “LASSO+Isomap”, the target variables were the leading two Isomap coordinates \({\mathbf {g}}({\mathbf {x}}) = \left( \phi _1({\mathbf {x}}), \phi _2({\mathbf {x}}) \right)\) , which reveal the phase angle \(\theta \) .
The sparsity-promoting regularization parameter was found using a bisection search in each case and was the smallest value, to within a tolerance of \(10^{-5}\) , for which group LASSO selected 3 sensors.
